The HERA accelerator at DESY in Hamburg was unique in that it smashed two totally different kinds of particles into each other – protons and electrons or positrons. HERA thus consists of two different accelerator rings: a superconducting proton ring (top) and a normal-conducting electron ring (bottom). HERA ran from 1990 to 2007
Photograph: DESY Hamburg

In the mid 1970s, four Soviet physicists, Batlisky, Fadin, Kuraev and Lipatov, made some predictions involving the strong nuclear force which would lead to their initials entering the lore. “BFKL” became a shorthand for a difficult-to-understand but important physical effect which could have big implications for high energy physics.

The strongest of the known fundamental forces of nature is something of an enigma. It holds together the nucleus of every atom – easily overcoming the electromagnetic repulsion between the positively-charged protons in there. The simplest atomic nucleus, that of hydrogen, is a single proton, but even that is held in one piece by the strong force, so tightly that it never falls apart – or at least, it lives billions of times longer than the current age of the observable universe. Truly, strong and stable.

We have a good theory of the strong force, which sits proudly in our Standard Model of particle physics. However, making predictions with this theory is very difficult. This is not simply to say that the sums are hard (they are), but that in many cases we don’t even know what sums we should be doing.

BFKL proposed, or discovered, a new set of sums which could be done using the theory behind the strong force. These sums should have a big effect on a particular type of particle collision, when very small fractions of the particle’s momentum are involved. If the energy of the colliding particles is high enough, this type of collision dominates all the others. So anything that has a big effect on these collisions is an important feature of nature, one that we would like to understand.

One striking feature of particles which are strongly interacting (like the proton) is that if two of them are approaching each other, the chance of them actually colliding increases as the energy of the particles increases. This behaviour was well-known experimentally, and was modelled in a precursor to the Standard Model called “Regge theory”¹. Amongst other things, the BFKL approach offered, for the first time, a chance of understanding this behaviour from first principles using the Standard Model.

Back in 1993, I was a fresh postdoc working on the HERA electron-proton collider which had just started operating at DESY in Hamburg. One thing we were on the lookout for was whether the features predicted by BFKL would show up in our data.

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The scattering probability for electrons and protons is generally expressed in terms of mathematical objects called structure functions, and the BFKL predictions said that one particular structure function should rise very rapidly as the fraction of the proton’s momentum involved in the collision got smaller.

We measured that structure function, and it did rise. But there were problems to sort out before declaring BFKL vindicated. The structure function did not rise as quickly as might have been expected by BFKL. It was also possible to explain the rise using different calculations – not featuring their sums. Most importantly, none of these calculations, by BFKL or others, was very precise, and nor were the data. We were in a grey area.

Over the years, many more data have come in, and better calculations have been made, by a generation of theorists and experimentalist wrestling with some formidable challenges. The qualitative impact of the BFKL sums is not now expected to be as dramatic as the initial calculations indicated, but it is still there, and still important.

A global analysis published on the arXiv this year by physicists from Amsterdam, Edinburgh, Genoa, Oxford and Rome pulls lots of this work together and makes the qualitative statements about the BFKL sums quantitative. Including these sums (in their newer and more precise form) gives a significantly better description of the data than is the case if they are omitted.

What this means is that we have pushed our understanding of the strong force into a new, previously unobserved region, and verified a qualitatively new emergent behaviour.

The formidable mathematics behind these calculations connects a deceptively simple underlying theory with a ubiquitous and counter-intuitive observational fact: scattering probabilities rise at high energies. This has implications for our understanding of many things, from the collisions at the Large Hadron Collider at CERN to the propagation and detection of high energy particles in cataclysmic cosmological events. It may even be important in understanding possible new strongly-interacting theories that may still to be discovered beyond the Standard Model.

There is more to be said about this physics, and I’m sure there will be further twists and turns. Still, this year we learned something about the basic materials of the universe we live in that we did not know before. The fact that we moved from not knowing to knowing over many years without a single identifiable “eureka” moment or sudden big announcement, doesn’t make the knowledge any less intriguing or significant.

¹Personally I’d say the Standard Model is more of a theory, while Regge theory is more of a model, but there we go.